Landau-Ginzburg Chern-Simons model with Ue(1)xUg(1) Gauge Symmetry and Internal Pseudo-Photons

In this article it is studied, at variational level, a mathematical setup given by the Landau-Ginzburg Chern-Simons model for anyons in 2+1-dimensions within the framework of dimensional reduced Ue(1)xUg(1) extended electromagnetism with both vector gauge fields (photons) and pseudo-vector gauge fields (pseudo-photons) such that both magnetic and electric vortexes coexist in the planar system. This model exhibits explicit planar P and T discrete symmetries being the Hall conductivity consistently a tensor and the Dirac quantization on the electric and magnetic coupling constants is equivalent to the quantization of magnetic flux. It is also discussed a thickening to 4-dimensions of the model with explicit 4-dimensional P violation which allows either for electric and magnetic charge separation, either for the Meissner effect. Although mathematically consistent, the electromagnetic field content for this model does not coincide with the standard Hall effect being present an extra orthogonal electric and longitudinal magnetic fields.